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Subwavelength spatial confinement of optical excitation in a doped solid

Neema S. Joseph

Published May 22, 2026• 0 citations
Publisher

Abstract

We experimentally demonstrated strong spatial confinement of optical excitations in Pr:YSO using two complementary coherent approaches: adiabatic passage techniques, namely STIRAP, double STIRAP, and tripod STIRAP, and broadband composite pulse (BCP) sequences. Both methods exploit the nonlinear response of coherent population transfer to transform a laser beam profile into a spatial filter, enabling localization of optical excitations far below the driving beam diameter. With conventional STIRAP, we achieved subwavelength localization down to 260 nm—only 2% of the pump beam diameter and more than a factor of two below the laser wavelength of 606 nm—representing a substantial improvement over previous demonstrations. At this confinement, the mean transverse ion occupancy drops below unity, placing our experiments in the single-ion addressing regime. Double STIRAP can further tighten confinement to below 1.4% of the beam diameter, albeit with loss of coherence due to the intermediate cleaning step, and can in principle be iterated for even stronger localization. Tripod STIRAP, by contrast, preserves coherence throughout the entire process while localizing population directly in a target state. In our experiment we achieved subwavelength confinement down to 350 nm, i.e., 3.5% of the control beam diameter, and crucially the sequential preparation of two-dimensional excitation patterns, demonstrated with grids of up to 41 individual spots without crosstalk between neighboring sites. To resolve these sub-imaging-resolution structures, we developed an autocorrelation-based measurement technique that showed excellent agreement with numerical simulations across all three STIRAP variants. As a second approach, we developed and implemented novel inhomogeneity-optimized BCP sequences tailored to the inhomogeneously broadened transitions of Pr:YSO. These sequences suppress the detuning-induced sideband artifacts that render previously proposed BCPs impractical in solid-state media, while maintaining high excitation efficiency over a wide range of pulse areas. Using IHO BCPs driven by a single donut-shaped laser beam, we confined optical excitations to 11% of the single-pulse excitation width—more than a factor of two improvement over previous narrowband composite pulse approaches, with a convergence rate of α = 0.68. We further tested BCP type II sequences that exploit variable pulse areas as additional control parameters, achieving localization down to 6% of the π-pulse excitation width at α = 0.95, albeit at the expense of increased detuning sensitivity. The current absolute widths of around 15 µm reflect the large beam waist chosen for imaging compatibility rather than a fundamental limit. Subwavelength confinement is readily achievable with tighter focusing. A systematic comparison of all techniques—including STED, RESOLFT, and EIT-based methods from literature—revealed that the coherent techniques developed in this work occupy a uniquely favorable region of capability space. STIRAP achieves the tightest relative confinement of any technique surveyed, which we attribute to the threshold nature of adiabatic passage and the resulting collapse of the numerator in the localization formula—a convergence channel unavailable to incoherent methods. Tripod STIRAP comes closest to satisfying all practical criteria simultaneously with coherence preservation, subwavelength confinement, demonstrated two-dimensional patterning, and long-lived storage. The CP approach complements these adiabatic techniques with single-laser simplicity and a direct path toward spatially selective quantum gate operations. Taken together, these results establish STIRAP-based techniques and BCP sequences as powerful and complementary tools for coherently preparing, addressing, and manipulating optical excitations on deep subwavelength scales. These capabilities are directly relevant to quantum memories, scalable qubit addressing in rare-earth crystals, and enhanced light–matter interactions at the nanoscale.

DOI
10.26083/tuda-8077

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arXiv:2111.03750•Optics Express•Mar 10, 2022•18 citations
We experimentally demonstrated strong spatial confinement of optical excitations in Pr:YSO using two complementary coherent approaches: adiabatic passage techniques, namely STIRAP, double STIRAP, and tripod STIRAP, and broadband composite pulse (BCP) sequences. Both methods exploit the nonlinear response of coherent population transfer to transform a laser beam profile into a spatial filter, enabling localization of optical excitations far below the driving beam diameter. With conventional STIRAP, we achieved subwavelength localization down to 260 nm—only 2% of the pump beam diameter and more than a factor of two below the laser wavelength of 606 nm—representing a substantial improvement over previous demonstrations. At this confinement, the mean transverse ion occupancy drops below unity, placing our experiments in the single-ion addressing regime. Double STIRAP can further tighten confinement to below 1.4% of the beam diameter, albeit with loss of coherence due to the intermediate cleaning step, and can in principle be iterated for even stronger localization. Tripod STIRAP, by contrast, preserves coherence throughout the entire process while localizing population directly in a target state. In our experiment we achieved subwavelength confinement down to 350 nm, i.e., 3.5% of the control beam diameter, and crucially the sequential preparation of two-dimensional excitation patterns, demonstrated with grids of up to 41 individual spots without crosstalk between neighboring sites. To resolve these sub-imaging-resolution structures, we developed an autocorrelation-based measurement technique that showed excellent agreement with numerical simulations across all three STIRAP variants. As a second approach, we developed and implemented novel inhomogeneity-optimized BCP sequences tailored to the inhomogeneously broadened transitions of Pr:YSO. These sequences suppress the detuning-induced sideband artifacts that render previously proposed BCPs impractical in solid-state media, while maintaining high excitation efficiency over a wide range of pulse areas. Using IHO BCPs driven by a single donut-shaped laser beam, we confined optical excitations to 11% of the single-pulse excitation width—more than a factor of two improvement over previous narrowband composite pulse approaches, with a convergence rate of α = 0.68. We further tested BCP type II sequences that exploit variable pulse areas as additional control parameters, achieving localization down to 6% of the π-pulse excitation width at α = 0.95, albeit at the expense of increased detuning sensitivity. The current absolute widths of around 15 µm reflect the large beam waist chosen for imaging compatibility rather than a fundamental limit. Subwavelength confinement is readily achievable with tighter focusing. A systematic comparison of all techniques—including STED, RESOLFT, and EIT-based methods from literature—revealed that the coherent techniques developed in this work occupy a uniquely favorable region of capability space. STIRAP achieves the tightest relative confinement of any technique surveyed, which we attribute to the threshold nature of adiabatic passage and the resulting collapse of the numerator in the localization formula—a convergence channel unavailable to incoherent methods. Tripod STIRAP comes closest to satisfying all practical criteria simultaneously with coherence preservation, subwavelength confinement, demonstrated two-dimensional patterning, and long-lived storage. The CP approach complements these adiabatic techniques with single-laser simplicity and a direct path toward spatially selective quantum gate operations. Taken together, these results establish STIRAP-based techniques and BCP sequences as powerful and complementary tools for coherently preparing, addressing, and manipulating optical excitations on deep subwavelength scales. These capabilities are directly relevant to quantum memories, scalable qubit addressing in rare-earth crystals, and enhanced light–matter interactions at the nanoscale.
We experimentally demonstrate subwavelength spatial confinement of optical excitation using variants of stimulated Raman adiabatic passage (STIRAP) in a Pr 3 + : Y 2 SiO 5 crystal. Building on conventional STIRAP, we implement two more advanced schemes, double STIRAP and tripod STIRAP, which enable enhanced spatial control. At the cost of reduced coherence, double STIRAP provides an almost twofold improvement in resolution compared with conventional STIRAP, which already enables localization nearly two orders of magnitude below the pump beam waist. To resolve such fine structures near the diffraction limit, we employ an autocorrelation-based measurement technique. With this setup, we demonstrate excitation confinement by conventional STIRAP down to 260 ± 40 nm , thus achieving subwavelength localization. As another powerful variant of adiabatic passage, we apply tripod STIRAP using an additional donut-shaped control beam that suppresses population transfer outside the beam center via coherent population trapping. With tripod STIRAP, we generate excitations as narrow as 350 ± 40 nm , a factor of 28 below the width of the driving control beam. We demonstrate the scalability of the method by preparing tightly packed grids with up to 41 excitation spots without crosstalk, making the method well-suited for quantum architectures. Our results establish STIRAP variants as robust, versatile tools for coherent, spatially selective optical excitation on a subwavelength scale, opening broad applications in quantum technologies and classical optics.
We experimentally demonstrate spatial confinement of optically driven atomic excitation by broadband composite pulses in a rare-earth ion-doped Pr 3 + : Y 2 SiO 5 crystal. The experimental data confirm that such sequences enable spatially localized excitation well below the diameter of the applied laser beam, with a substantial improvement compared to previous developments and applications of other classes of composite pulses. In particular, we derived and applied broadband composite sequences, which also work efficiently in inhomogeneously broadened media, while also maintaining robustness with regard to fluctuations of the driving laser intensity. We perform extensive measurements to assess and compare the performance of several classes of broadband composite sequences. The findings are confirmed by numerical simulations, which agree very well with the experimental data. As the concepts are also applicable to spatially confined excitations below the diffraction limit of the laser beam, the results serve as an important step towards high-resolution imaging, preparation and addressing in quantum technologies and classical applied optics.
Abstract We experimentally demonstrate spatial confinement of atomic excitation by adiabatic passage processes in a rare-earth ion-doped Pr3+:Y2SiO5 crystal. In particular, we apply stimulated Raman adiabatic passage (STIRAP) and compare its performance with electromagnetically induced transparency (EIT). Using a Stokes beam with Gaussian and a pump beam with donut shape we localize the atomic population in the zero-intensity center of the latter. Our data confirm that adiabatic passage confines excitation far below the diameter of the driving laser beams, and that this localization rapidly increases with laser intensity. We find, that STIRAP significantly outperforms EIT, as it was predicted by previous theory proposals, i.e., STIRAP reaches small excitation volumes with much lower laser intensity. The experimental data agree very well with numerical simulations. The findings serve as a step towards new applications for STIRAP, to prepare excitation regions or population patterns in space with large resolution.
We experimentally demonstrate spatial confinement of atomic excitation by narrow-band composite pulse (NCP) sequences in a rare-earth ion-doped Pr3+:Y2SiO5{\text{Pr}}^{3+}\text{:}{\text{Y}}_{2}{\text{SiO}}_{5}Pr3+:Y2​SiO5​ crystal. The experimental data confirm that NCP sequences localize excitation far below the diameter of the driving laser pulse, with potential to proceed below the diffraction limit. We reach significant improvement of the spatial confinement compared to previous implementations. To this end, we derive several new classes of composite pulses that significantly outperform previously known sequences for the objectives of this study. In particular, the new NCP sequences are applicable also in inhomogeneously broadened ensembles, where most conventional composite pulse sequences fail. We systematically investigate the performance of the different classes of sequences and compare the results with numerical simulations, which agree very well with our experimental data. The findings serve as a step towards novel applications of composite pulse sequences to precisely prepare and manipulate excitation patterns in space, e.g., in quantum technology to address qubits with large spatial resolution.
The present work deals with techniques to improve the EIT-based light storage in an all solid-state memory, i.e. a rare-earth ion-doped PrYSO crystal. The performance of such a memory can be defined by its capability to store light pulses with high efficiency and for long storage durations. In general, the storage efficiency is theoretically limited by the EIT-LS protocol efficiency, while the storage duration is limited by decoherence processes in the solid-state memory. Thus, we first optimized the EIT-LS efficiency at short storage durations. We then investigated the performance of composite and adiabatic techniques for efficient and robust rephasing and finally applied composite techniques for DDC to extend the coherence lifetime in our storage medium. Optimization of the EIT Light Storage Efficiency: In order to optimize the EIT-LS protocol we performed systematic measurements of the EIT-LS efficiency in a PrYSO crystal featuring an optical depth d of 6. The optical depth sets the theoretical limit of the EIT-LS protocol efficiency. We experimentally optimized the efficiency by systematic variations of the control pulse power and the probe pulse duration. Furthermore, we applied an iterative algorithm, to optimize the temporal shape of the probe pulse. We found a maximal protocol efficiency 36 %, comparable to the theoretical limit. In order to increase the optical depth d, we developed a multipass setup for the probe beam, consisting of a ringlike arrangement, which is compatible with the geometrical constraints given by the existing setup. This multipass setup allows the simple variation of the number of probe passes N through the crystal and thus enables a flexible change of the effective optical depth. With this setup we achieved up to 16 probe passes through the PrYSO crystal, which corresponds to an increase of the effective optical depth from 6 to 96. We experimentally optimized the EIT-LS efficiency at variable optical depths. At N=14, i.e. an effective optical depth of about 84, we achieved an EIT-LS efficiency of 76.3 % in forward retrieval configuration, reaching previous values in an EIT-driven memory of cold atoms and achieving the highest ever obtained EIT-LS efficiency in a solid-state memory. However, due to losses at the optical components, the setup efficiency was limited to about 25.2 % at N=2. As future work will focus on the storage of few photons, it will thus be necessary to improve the optical components, to achieve adequate detection efficiencies. It might also be useful, to further investigate possibilities for backward readout configurations combined with a multipass probe setup. Composite and Adiabatic Rephasing of Atomic Coherences: In order to extend the EIT-LS duration of our memory towards the coherence lifetime, we implemented composite and adiabatic rephasing techniques, exhibiting an improved robustness regarding variations and fluctuations of experimental parameters. We investigated their performance regarding experimental variations, in an application for rephasing of atomic coherences in the inhomogeneously broadened hyperfine transition of PrYSO. First, we applied universal composite pulses (UCP). UCP were originally designed for robust and high-fidelity population inversion in a two-state system, compensating simultaneous variations in any type of experimental parameter. We have experimentally shown that UCP exhibit an enhanced robustness to variations in several experimental parameters. Using UCP we could increase the higher rephasing efficiency about 25 %, compared to diabatic π pulses. UCP can be useful whenever significant unknown experimental variations or fluctuations prevent the application of diabatic π pulses. Second, we demonstrated a first experimental implementation of composite adiabatic passage (CAP). Essentially, CAP is a composite version of RAP, consisting of a sequence of RAP pulses with appropriately chosen relative phases. CAP was proposed to improve RAP in situations of fairly fulfilled adiabaticity. We compared the performance of CAP and RAP at different degrees of adiabaticity. In particular, we systematically investigated their performance with respect to variations in pulse duration and static detuning. We found CAP to be able to compensate for weak adiabaticity, leading to constant and high rephasing efficiency, irrespectively of the exact choice of the experimental parameters. These properties of CAP can be of interest whenever robust state manipulations are required, while sufficient adiabaticity cannot be provided, e.g. due to experimental restrictions. Third, we performed a first experimental demonstration of single-shot shaped pulses (SSSP), derived from techniques on shortcuts to adiabaticity. We demonstrated the capability of SSSP for efficient and robust rephasing and compared our results with diabatic π pulses. A further comparison with other adiabatic techniques might be necessary to provide a broader insight on SSSP. All three presented techniques can be used to improve the robustness of an population inversion or rephasing process. However, different requirements on the control of the experimental parameters have to be fulfilled. UCP, and CAP rely on identical pulses and a precise relative phase control, i.e. within a few degrees. CAP in addition needs a simple control of the time-dependent detuning. The complex time-dependent Rabi frequency and detuning of SSSP require a much more sophisticate control of experimental parameters. Thus, the choice of an adequate technique strongly depends on the actual experimental situation, i.e. on the experimentally controllable parameters. Composite Pulses for Dynamic Decoherence Control: We investigated the performance of UCP and universal robust (UR) sequences for DDC of directly RF-prepared coherences. We compared our results with well known CPMG DD and KDD sequences. We performed systematic measurements with respect to the cycling time, the phase of the coherence and the order of UCP and UR DD sequence. We found time separated UR DD sequences to be robust with respect to the phase of the coherence. We applied these DD sequences on EIT-LS coherences and compared with CPMG DD and KDD in XY4. Our experiments showed that our UR DD sequences can outperform the often considered state-of-the-art KDD in XY4 sequence, yielding about a factor of 2 longer coherence lifetimes. Combining our results on optimized EIT-LS with advanced composite DD sequences and static decoherence control by ZEFOZ might provide a major step towards the development of an all solid-state quantum memory.
We consider a method of sub-wavelength superlocalization and patterning of atomic matter waves via a two dimensional stimulated Raman adiabatic passage (2D STIRAP) process. An atom initially prepared in its ground level interacts with a doughnut-shaped optical vortex pump beam and a traveling wave Stokes laser beam with a constant (top-hat) intensity profile in space. The beams are sent in a counter-intuitive temporal sequence, in which the Stokes pulse precedes the pump pulse. The atoms interacting with both the traveling wave and the vortex beam are transferred to a final state through the 2D STIRAP, while those located at the core of the vortex beam remain in the initial state, creating a super-narrow nanometer scale atomic spot in the spatial distribution of ground state atoms. By numerical simulations we show that the 2D STIRAP approach outperforms the established method of coherent population trapping, yielding much stronger confinement of atomic excitation. Numerical simulations of the Gross-Pitaevskii equation show that using such a method one can create 2D bright and dark solitonic structures in trapped Bose-Einstein condensates (BECs). The method allows one to circumvent the restriction set by the diffraction limit inherent to conventional methods for formation of localized solitons, with a full control over the position and size of nanometer resolution defects.